This article analyses the meaning and procedure, in the Spanish legal system, of the causes resulting on denial of recognition and enforcement of a foreign Award, due to «differences» that cannot be solved through arbitral proceedings. This is settled by means of the arbitrability of the subject matter and its relation to public order in the country where it is to be enforced. Nonetheless, this scheme is not without difficulties, indicates the author. Various precepts apply and their interaction sets the analysis of articles 2.1 LA, 9.6 LA, art. V.1a) of the New York Convention as well as art. 62 of the Spanish Civil Code. Finally, it addresses some issues related to Case Law within the context of the article.